Martingale calculator: stake ladder, odds and expected loss

How the figures are worked out

The Martingale here plays by the app's own rules: an even money bet on red, the base bet first, doubled after every loss and back to the base after every win. Before every spin the table limit is checked first and the bankroll second, and a bet the table refuses or the bankroll cannot cover ends the session. A bet is never cut down to fit what is left, and nothing is borrowed. The base bet has to meet the table minimum too, which is 5 points on red at the app's standard table.

Each bet is double the one before, so after a run of losses the next bet is always one base bet more than everything the run has lost: once 5, 10, 20, and 40 have lost 75, the next bet is 80. The bankroll carries the ladder as long as everything the run has staked fits in it, and the table limit as long as each bet stays within the limit; whichever stops it sooner ends the session. With 500 points and a base bet of 5 the bankroll covers 6 bets, 315 points in all, and the next one, 320, is more than the 185 left; the limit of 1,000 alone would have allowed 8.

Every cycle from the base bet ends with a win, one base bet up, loses every step of the ladder, or is cut off by the end of the session. On a single zero wheel red loses 19 spins in 37, the zero included, so a whole ladder of 6 bets loses with a chance of 19/37 to the power of 6: 1.83%, about 1 in 55. So each cycle risks 315 points to win 5.

The chances for the whole session are exact, not simulated. Between spins all that matters is how many wins the session has had and how many losses in a row it is on, and from there a spin wins with a chance of 18 in 37 and loses with 19 in 37. The calculator follows the chance of every such position from spin to spin, takes out each one where the table or the bankroll refuses the next bet, and adds up how every possible session ends. A session whose last spin completes the losing run counts as having met it, even though no further bet is asked for. Because each win adds a base bet to the bankroll, a session that has won enough can take more steps, and the chances count that too.

Every bet on red returns 36 points for every 37 staked on average, so the house keeps 1 in 37, 2.70%, of everything staked, whatever the size of the bet. The expected result is the average total staked divided by 37, as a loss: in the worked example an average of 1,161.30 points is staked over 100 spins, so the expected loss is 31.39 points. Doubling changes how the losses are spread out, never the 1 in 37 of every point staked that the house keeps.

What the numbers mean

A Martingale wins one base bet at a time, again and again, which is what makes it feel safe: in the worked example the chance of ending the session ahead is 49.17%. The sessions that meet the losing run pay for all of those wins and more. A bigger bankroll or a higher table limit can make the run rarer, but the loss is larger when it comes, and the expected result stays a loss of 1 in 37 of everything staked. No betting system overcomes the house edge: this calculator shows the risk, not a way to win.

The Martingale page shows how the simulated sessions with the worked example's settings went. They land close to the exact figures here; the share that ran out of points there is a little lower than the chance of meeting the run here, because a run completed on the very last spin does not end a session early. The Grand Martingale page shows a ladder that climbs faster still, and for what any single bet pays and costs there is the roulette payout calculator.

Common questions

How many losses in a row can a Martingale survive?

One fewer than the bets on its ladder. With 500 points and a base bet of 5 the ladder has 6 bets: after 5 losses in a row the 6th bet can still win everything back, and if it loses too, the session ends 315 points down.

What is the chance of losing 6 times in a row on red?

On a single zero wheel red loses 19 spins in 37, the zero included, so the chance of 6 losses in a row over any 6 given spins is 19/37 to the power of 6: 1.83%, about 1 in 55. A session of 100 spins has many such stretches. Each win also adds a base bet to the bankroll, so after 27 wins it covers a 7th bet and 6 losses in a row no longer end the session; counting that, the chance of meeting a losing run the session cannot cover is 50.38%.

Does a bigger bankroll make the Martingale safe?

No. With 1,000 points instead of 500 the ladder has room for 7 bets: the chance of meeting the losing run in 100 spins becomes 36.24%, but the run now costs 635 points, and the expected result falls to -40.49 points from -31.39. Every bet still loses 1 in 37 of its stake on average.